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MNRAS 474, 933–946 (2018) doi:10.1093/mnras/stx2663 Advance Access publication 2017 October 24

WD 1145+017: optical activity during 2016–2017 and limits on the -ray flux

S. Rappaport,1‹ B. L. Gary,2‹ A. Vanderburg,3,4‹† S. Xu(),5 D. Pooley6 and K. Mukai7,8 1Department of , Kavli Institute for Astrophysics and Research, M.I.T., Cambridge, MA 02139, USA 2Hereford Arizona Observatory, Hereford, AZ 85615, USA 3Harvard–Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 4Department of , The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA

5European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 6Department of Physics and Astronomy, Trinity University, San Antonio, TX 78212-7200, USA 7CRESST and X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 8Department of Physics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

Accepted 2017 October 10. Received 2017 October 6; in original form 2017 August 19

ABSTRACT WD 1145+017 was observed from 2016 November through 2017 June for the purpose of further characterizing the behaviour of the dusty debris orbiting this . The optical observations were carried out with a small ground-based run by an amateur , and covered 53 different nights over the 8-month interval. We have found that the optical activity has increased to the highest level observed since its discovery with Kepler K2, with approximately 17 per cent of the optical flux extinguished per . The source exhibits some transits with depths of up to 55 per cent and durations as long as 2 h. The dominant period of the orbiting dust clouds during 2016–2017 is 4.49126 h. We present ‘waterfall’ images for the entire 2016–2017 and 2015–2016 observing . In addition, the white dwarf was observed with the X-ray Observatory for 10-ks on each of four different occasions, separated by about a month each. The upper limit on the average X-ray flux from WD 1145+017 is 5 × 10−15 cm−2 s−1 (unabsorbed over the range 28 0.1–100 keV), which translates to an upper limit on the X-ray luminosity, Lx,of 2 × 10 −1 erg s .IfLx GMwdM˙ acc/Rwd, where Mwd and Rwd are the mass and radius of the white 11 −1 dwarf, and M˙ acc is the rate, then M˙ acc  2 × 10 gs . This is just consistent with the value of M˙ that is inferred from the level of dust activity. Key words: planets and : composition – planets and satellites: detection – planets and satellites: general – planet– interactions.

−1 1 INTRODUCTION 300 km s (Xu et al. 2016). The of the discovery of WD 1145+017, a review of its properties and some ideas about the WD 1145+017 is a unique white dwarf that has the following four orbiting debris are given in the review of Vanderburg & Rappaport attributes: it (1) exhibits atmospheric pollution via an array of (2017, and references therein). Some of the basic photometric and lines (Vanderburg et al. 2015; hereafter ‘V15’; Xu et al. 2016); (2) spectroscopic properties of the object are summarized in Table 1. shows strong evidence for a dusty disc that produces IR emission in A substantial fraction of white dwarfs exhibit atmospheric pollu- excess of the white-dwarf’s intrinsic emission (V15); (3) exhibits tion from metals such as Mg, Al, Si, Ca, Ti, Cr, Mn, Fe and Ni. This deep transits that are thought to be due to orbiting disintegrating observation, coupled with the relatively short gravitational settling debris (V15;Gansicke¨ et al. 2016; Rappaport et al. 2016, hereafter times, suggest that there must be a nearly continual process of accre- ‘R16’; Gary et al. 2017, hereafter ‘G17’) and (4) has broad and tion (e.g. Zuckerman et al. 2010;Koester,Gansicke¨ & Farihi 2014). variable circumstellar metal absorption lines with widths of up to A smaller fraction (perhaps ∼3 per cent) of all white dwarfs and up to 20 per cent of polluted white dwarfs (Zuckerman & Becklin E-mail: [email protected] (SR); [email protected] (BLG); avanderburg@ 1987) are also found to have NIR signatures of dusty discs orbiting utexas.edu (AV) them (Kilic et al. 2006; Farihi, Jura & Zuckerman 2009;Barber † NASA Sagan Fellow. et al. 2012; Rocchetto et al. 2015).

C 2017 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society 934 S. Rappaport et al.

Table 1. Photometric and spectral properties broad metal absorption lines may be due to gas, produced from of WD 1145+017. sublimated dust and orbiting close into the white dwarf, perhaps within ∼10 Rwd (Xu et al. 2016; Redfield et al. 2017; Vanderburg Parameter WD 11145+017 & Rappaport 2017). RA (J2000) 11:48:33.627 In this paper, we discuss the results of optical monitoring of WD Dec. (J2000) +01:28:59.41 1145+017 covering 8 months of the 2016–2017 observing . Spectral type DBZA We also present the results of four Chandra X-ray observations of a Kp 17.29 10 ks each, but spanning an interval of 20 weeks. In Sections 2 and 3, gb 17.00 ± 0.01 we describe how the optical and X-ray observations were acquired. Jc 17.50 ± 0.03 The results of the optical observations are presented in Section 4, Kc 17.40 ± 0.08 including a number of illustrative light curves (Section 4.1), a new W1d 17.02 ± 0.16 way to visualize ‘waterfall’ diagrams (Section 4.2), a search for W2d 16.51 ± 0.35 periodicities (Section 4.3) and an overview of the photometric dip

e ± Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 Teff (K) 15 900 500 activity since its discovery (Section 4.4). The Chandra X-ray ob- e ± logg (cgs) 8.0 0.2 servations led to only an upper limit on the flux which is evaluated Re ± wd(R⊕)1.400.18 Me ± and discussed in Section 5. An interpretation of what this limit on wd(M)0.590.12 e ± the X-ray flux implies for the accretion rate of debris is explored Cooling age (Myr) 175 75 + Distance (pc)f 174 ± 25 in Section 5.4. Our current understanding of WD 1145 017 is dis- − μα (mas yr 1)f −43.3 ± 4.9 cussed more broadly in Section 6. We summarize our results and − μδ (mas yr 1)f −7.0 ± 4.9 draw some final conclusions in Section 7. Orbital periodg (hr) 4.49126 Orbital radiusg (R)1.16 2 GROUND-BASED OPTICAL MONITORING Notes. ahttps://archive.stsci.edu/k2/epic/search.php. bTaken from the SDSS image (Ahn We report on 53 observing sessions of WD 1145+017 during the et al. 2012). 8-month interval 2016 October 25 through 2017 June 18. The me- cUKIDSS magnitudes (Lawrence et al. 2007). dian interval between observing sessions was 4 d. dWISE point source catalogue (Cutri All observations were made with the Hereford Arizona Obser- et al. 2013). vatory (HAO, Center site code of G95). This is a e V15; http://dev.montrealwhitedwarfdatabase.org/ private observatory in Hereford, Arizona, consisting of a 14-inch .html (Dufour et al. 2017). Meade LX200 GPS telescope and a Santa Barbara Instrument Group fFrom UCAC4 (Zacharias et al. 2013); Smart (SBIG) ST-10XME CCD camera. All observations were unfiltered; & Nicastro (2014). gBased on the periodicity observed the system response exceeded 10 per cent of maximum from 400 in this work. to 900 nm. The telescope, camera, filter wheel, autoguiding sys- tems and dome azimuth are controlled from a residence office via WD 1145+017 has all these attributes, but what makes it unique buried 100-feet cables. A commercial program, MaxIm DL v5.2, are (i) the transits that are presumed to be due to dust clouds in is used for observatory control as well as later image processing. 4.5–5 h (V15;Gansicke¨ et al. 2016 ; R16; G17), and (ii) the Calibration images (bias, dark and flat) are updated at appropriate very broad absorption lines ascribed to high-velocity metal gases intervals, with emphasis on using the same CCD camera control orbiting perhaps even closer to the white dwarf (Xu et al. 2016; temperature for dark frames. Autoguiding was usually performed Redfield et al. 2017). The details of the orbiting debris that produces using the ST-10XME second chip (meant only for autoguiding) in the dust, in particular the numbers and masses of the bodies, are order to preserve the star field’s pixel location throughout each ob- largely unknown. However, in broad brush, there were six distinct serving session. Once an observing session is set up and operating periods found in the K2 discovery observations ranging from 4.5 to in a stable manner, the observatory is allowed to function for the 4.9 h; these were named the ‘A’ through ‘F’ periods. Periods within rest of the night unattended; automatic shut-down of hardware is ∼0.2 per cent of the A period found in K2, have been seen in ground- accomplished when specified conditions are met (elevation <15◦, based observations ever since the transits were first discovered. astronomical twilight, etc.). The ‘B’ period, at 4.605 h, was detected briefly, and convincingly, The image processing, using MaxIm DL, is maintained as close as during the 2015–2016 observing season. The other periods have possible to the same procedure for all observing sessions throughout not yet been detected from the ground. However, the transit depths the entire observing season. All images are calibrated, and then measured with K2 for the ‘C–F’ periods were largely below the star aligned. An artificial star is placed in the upper-left corner of level of what can be detected from the ground. All of the periods each image for the purpose of converting the tool’s detected correspond to Keplerian orbital radii close to ∼100 white- measurements to flux (since MaxIm DL v5.2 does not dwarf radii, or approximately 1 R. permit saving flux information). The photometry tool is used to While relatively little detail is known about the numbers, masses specify WD 1145+017 as the ‘target’, the artificial star is specified and of the orbiting bodies in WD 1145+017, a variety of as a reference star and 25 nearby are specified as ‘check stars’. studies have been carried out in an effort to understand the transit The photometry target circle radius is set to 4 pixels (7 arcsec), the properties (depths, rates, evolution, etc.). These include dynamics gap annulus width is set to 3 pixels and the background annulus of multiple bodies in close orbits, sublimation rates and dust produc- width is set to 12 pixels; photometry readings are saved as text files. tion, tidal disintegration of and collisional cascades (see, The photometry signal circle radius is also changed to 3 and 5 pixels, e.g. V15; R16; Veras et al. 2016; Gurri, Veras & Gasicke¨ 2017; and these two additional photometry data files are saved. Kenyon & Bromley 2017). The masses of the dust-producing bod- The rationale for the preceding steps, and those to be presented ies have been estimated to range between 1017 and 1023 grams. The next, are described in the book Observing for Amateurs

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Table 2. Chandra observations of WD 1145+017.

Date (JD) Date (UT) Obs. ID Exposure (ks)

2457802.3 2017 February 17 18917 10.4 2457850.1 2017 April 6 18918 9.9 2457902.0 2017 May 28 18919 9.9 2457939.1 2017 July 4 18920 9.9 Total ∼20 weeks – 40.2

(Gary 2014). The procedures were developed during 15 yr of exo- unknown time delay between the release of dust in the system, and planet observing and the similarities with the WD 1145+017 light- the subsequent accretion of the sublimated gas from that dust. Thus, curve generation made it an obvious choice for this work. we elected to search for X-ray emission over a range of different Each of the text files with photometry readings is imported to times. Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 a spreadsheet specifically meant for use with WD 1145+017. For The Chandra proposal was accepted and the observations were each of the three photometry target circle radius readings, a calcu- carried out during February, April, May and July of 2017. Each lation is made of the rms(t) variations using a neighbour-difference observation was 10 ks in duration, for a total exposure of 40 ks. The method. A weighted average of the three photometry readings is dates of the observations are summarized in Table 2. calculated; this achieves most of the optimization that would be The observations were made with ACIS-S (of the Advanced CCD accomplished if one photometry reading was made with a dynamic Imaging Spectrometer) using the back-illuminated S3 chip in imag- photometry aperture size, so the resultant set of weighted-average ing (i.e. non-grating) mode. We utilized the timed exposure (TE) and magnitudes are less affected by atmospheric seeing changes to the very faint (VF) source modes, and with no subarrays. The on-board point spread function (full width at half-maximum size) during the energy filtering range was 0.24–12 keV. observing session. The user manually solves for atmospheric ex- tinction, including a temporal trend term, with the aid of graphs. 4 RESULTS OF THE OPTICAL STUDIES Departures from the extinction model reveal when clouds were present, as well as other anomalies (such as large seeing degrada- 4.1 Light curves tions). A special method is used to automatically identify artefacts in the During this past observing season (2016–2017), the dips in the 25 stars (identified within MaxIm DL as ‘check’), such as cosmic optical flux from WD 1145+017 were no deeper than during the ray hits, and these specific star readings are disregarded in a process previous season, but they were numerous, often resulting in effec- that produces total flux for all (accepted) check stars; the final total tively very long (1.5–2 h) transits. In net, the dips produced the flux versus UT is treated like a ‘reference star’. Graphical displays highest ‘activity’ level seen since the source’s discovery as a white provide a means for quickly identifying stars that are unexpectedly dwarf undergoing periodic transits (V15). As much as 17 per cent variable (or saturated, and therefore not suitable for use); the user of the average flux during a 4.5-h period was missing in January can toggle ‘use/do not-use’ spreadsheet switches for each of the (see Fig. 7). 25 stars. The use of ‘sum of flux’ for all accepted stars for ‘refer- In Fig. 1, we show four illustrative light curves recorded in ence’ is superior to averaging magnitudes, as is done by standard November, January, February and of this past 2016–2017 differential photometry. observing season. Except for the November observation, the light The resulting WD 1145+017 magnitudes are assigned standard curve covers a full orbital cycle recorded during a single night, and errors (‘SE’) uncertainties by calculating rms(t) for several of the is plotted against orbital phase using a common period of 4.49126 h 25 stars used for reference, and a model for rms versus instru- (see also Croll et al. 2017), and an epoch of JD 2457687.7335. In ment magnitude is used for predicting the WD 1145+017 SE. A all cases, there is a portion of the flux dip that lasts for at least neighbour-difference method (Gary 2014) is used for calculating 0.3 orbital cycles, and in two cases for nearly half an orbital cy- rms(t) for the reference stars. cle. The dips in flux range in depth, at their deepest points, up to The spreadsheet analysis procedure is not meant for automatic 55 per cent, but were never seen to go deeper than 55 per cent at implementation, as it requires user judgement at many steps. How- any time during this season’s observations. The solid curves super- ever, most decisions are guided by objective calculations to min- posed on the data are fits to sums of asymmetric hyperbolic secants imize subjective bias while assuring data quality. Because of this (‘AHS’) that we have discussed in our previous work (R16; G17). extra attention, and because the ST-10XME CCD has high QE They are meant to (i) guide the eye, (ii) assess quantitatively the (87 per cent), it has been estimated that the HAO 14-inch telescope area under the dip and (iii) track phase drifts of different persistent system performs like a typical 17-inch telescope. features. In order to better visualize how the light curves evolve over time- scales of days to weeks, we show some illustrative examples in 3 CHANDRA X-RAY OBSERVATIONS Fig. 2 of evolving light curves during the intervals 2017 January Because of the possibility of observing X-rays from the inferred 22–February 8, and March 22–April 5. In each case, we show the accretion of material on to the white dwarf in WD 1145+017, we AHS fits to the light curves on four different days that span an proposed Chandra observations in Cycle 18. We requested expo- interval of about two weeks. These curves are all phased to the sures of 10 ks to be carried out on four different occasions to be same period (4.49126 h) using approximately the same epoch of separated by at least one month. We did this because (i) it was phase zero as that in Fig. 1. Fig. 2 serves to show how, on the one difficult to predict in advance when WD 1145+017 would be most hand, the dip features are quite repeatable from to day, while on active in terms of exhibiting dust extinctions, and (ii) there is an the other hand, how they do clearly evolve on time-scales of weeks.

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Figure 1. Four light curves of WD 1145+017 showing normalized flux for each image (small circles) and a fitted model (red curve; see the text). Note the deep (up to 50 per cent) and very long dips which were not present during the last three observing seasons. The light curves are phased to a period of 4.49126 h and epoch of phase zero at BJD 2457687.7335.

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Figure 2. Superpositions of fits to four different light curves covering the interval JD 2457834−48 (top panel) and JD 2457775−92 (bottom panel). The fits are each to the light curve from a single night. They are presented in lieu of the data themselves to promote clarity and minimize confusion. The same period and epoch are used here as in Fig. 1.

4.2 Waterfall diagrams of the observation. We then applied a simple algorithm to fill in the gaps, as follows. For each point in the image, if there exists a data Perhaps the best way to obtain an overview of the dip activity in WD point, we leave it as it is. If a pixel is initially blank, we draw a 1145+017 over an observing season is to study a ‘waterfall’ type circle around that point which is 10 pixels in radius (corresponding diagram. In previous work, we have produced waterfall diagrams to 7 min in phase, and 5 d on the calendar), and take a distance by (i) stacking traces of the flux versus orbital phase in order of weighted average of all the points within which there are data. The observation date (see, e.g. fig. 1 of R16;alsofig.1ofGansicke¨ weighting was done according to d−2,whered is the distance be- et al. 2016), and (ii) reducing each fitted dip to a bar whose length tween the point being ‘filled’ and the data points (in units of pixels). is the dip duration, and thickness is the dip depth (e.g. fig. 6 of R16; Specifically, the flux used to fill the blank bin is given by fig. 4 of G17). In this work, we attempt a new approach that we believe presents  F d−2 a more coherent picture of the source activity. The waterfall di- m=n mn mn Fn =  , (1) −2 agram nominally indicates the orbital phase along the x-axis and m=n dmn observation date along the y-axis. We have constructed a waterfall- diagram ‘image’ of 400 × 400 pixels where the intensity in each where m is any other point within 10 pixels of n. pixel represents the measured flux at a specific moment. Each pixel What we see from the resultant waterfall plot based on data from in the x direction represents 40 s in orbital phase (comparable to the 2016–2017 season is that many of the features have a period the cadence of the observations) while each pixel in the y direction close to 4.49126 h. That this is the case can be understood from the corresponds to a half day on the calendar. fact that features in the image with this period tend to run vertically. The results for the 2016–2017 season are shown in Fig. 3.The Just to indicate the sensitivity of such a plot to periods that may challenge was to fill in the quite substantial gaps where no ob- differ from the fold period, we point out that a feature lying at a servations were conducted. As mentioned above, the median gap 45◦ angle represents a period difference of P/P +0.001. In the between observations was about four nights. In addition, some of right-hand panel of Fig. 3, we have numbered six of the dip features the observations early and late in the season suffered from shortened that seem to persist for intervals of days to months. We emphasize, windows of target visibility. We handled the data gaps as follows. however, that via these diagrams alone there is not a robust way The flux from each observation was placed into the appropriate to uniquely identify the separate features, and the ones we have {x, y} bin according to the phase of the 4.5-h period and the date numbered are subjective.

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Figure 3. WD 1145+017 waterfall diagrams for the 2016–2017 season. These were produced from the light curves obtained on 53 individual nights, and then interpolated to fill in the regions where data are missing (see the text for a discussion of the interpolation method). The right-hand panel is the same figure, but with various features numbered for discussion in the text. The colour-coding represents the normalized source brightness, with yellow-orange regions being near full intensity, while the darkest regions have only ∼50 per cent of the full brightness. The period used to phase both diagrams is 4.49126 h, and the epoch of phase zero is taken, somewhat arbitrarily, to be BJD 2457687.7335.

Here, we describe more specifically the various numbered dip features in Fig. 3. Feature 1 is mostly a straight vertical line, but with some kinks or bends. The smallest discernible curvatures cor- respond to P/P˙ 2000 yr. Feature 2 exhibits a large degree of curvature – corresponding P/P˙ 400 yr. Feature 3 is ‘highly’ sloped with a period of 4.498 h versus the 4.49126 h used to make the fold. Feature 4 is a new dip that also starts around day 40 and ends around day 180. Initially, at least it seems to have the same period as Feature 1, but simply appears at a different orbital phase. Feature 5 seems to be a new dip feature that appears around day 20 of the plot and ends about two months later. Feature 6 starts at about day 170 and persists until the end of the observations. It may have a period that is similar to that of Feature 3. One thing that should be kept in mind about these features is that they all have orbital periods within a range of 0.1 per cent. The longest period, 4.4953 h, is close to the K2 ‘A’ period at 4.4989 h. We next went back to the photometric data that we had collected during the previous observing season (2015–2016) and utilized the same algorithm to construct the corresponding waterfall plot. The results are shown in Fig. 4. The fold period and epoch of the fold are the same as used to produce Fig. 3. Many of these features were discussed extensively in G17, so we will point out only the most salient features. First, there is a prominent vertical stripe that appears to be closely connected to Feature 1 in Fig. 3; it may very well be the same underlying body, in a 4.49126 h period, that accounts for Figure 4. WD 1145+017 waterfall diagram for the 2015–2016 season. both these features in Figs 3 and 4. The second set of prominent Other descriptors are the same as for Fig. 3. The period used to phase both features are the three sets of dips that run at roughly an angle of diagrams is 4.49126 h, and the epoch of phase zero is taken, somewhat 25◦ from horizontal. These correspond to a period of 4.499 h (very arbitrarily, to be JD 2457687.7335. close to the K2 A period), but with a wide range of orbital phases for the three sets of dips. Finally, there is a feature that seems to begin abruptly on day 140 and phase 0.65. This is in fact the event 4.3 Search for periodicities denoted as ‘G6420’ in G17, and shown in greater detail in fig. 6 of In order to search for periodicities that might be persistent, but of G17. too low an amplitude to show up in the waterfall diagram (Fig. 3),

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Figure 6. Flux data from WD 1145+017 folded about a period of 4.49126 h. The black dots are the individual data points, while the heavy black curve represents a smoothed profile.

identified because individual transits were seen by eye, and was not found via a periodicity search. Finally, in regard to the principal period found in this data set, we show in Fig. 6 a fold of all the 2016–2017 photometry data about a period of 4.49126 h.

4.4 Activity level of WD 1145+017 We have collected all of the data available to us on the source ‘ac- tivity’ since it was discovered (V15). The ‘activity’ level is defined formally by equation 1 of G17, but is essentially just the integrated Figure 5. Periodograms of the WD 1145+017 optical flux data for the dip depth over one orbital cycle. We show an updated version of 2016–2017 observing season. Top panel: L-S transform. Bottom panel: the activity level diagram, including this entire current observing BLS transform. The principal periods detected are 4.4922 ± 0.0003 h in season, in Fig. 7. Note that, at times during this past season, the the L-S transform and 4.4912 ± 0.0004 h in the L-S transform. Most of the activity level has been two orders of magnitude greater than during other significant peaks are 1-d aliases of the principal period, or its higher the K2 discovery observations. On average, the source has been harmonics. twice as active this season compared to last season. we carried out both a Lomb–Scargle (Lomb 1976; Scargle 1982) 5 INFERENCES FROM LIMITS ON X-RAY as well as a Box Least Squares (Kovacs,´ Zucker & Mazeh 2002) FLUX periodogram search. In each case, we used all of the ground-based optical photometry data taken during the 2016–2017 season, sub- 5.1 X-ray image tracted the mean flux and then subjected the resultant data set to these transforms. As discussed in Section 3, there were four 10-ks Chandra exposures The results are shown in Fig. 5. The top panel shows the L-S of WD 1145+017 during the period 2017 February 17–July 4. The transform. The centroid of the most prominent peak is at 4.4922 h times of the four Chandra exposures, relative to the optical activity, with a nominal width of 0.004 h. Given that this peak is detected are shown as arrows on the activity plot (Fig. 7). As is obvious at about the 15σ level, we estimate the uncertainty in the period at from the plot, three of the four exposures were taken at among the ∼0.0003 h. All the other significant peaks in the L-S transform are highest dust-activity levels known since the source was discovered. either aliases of the 1-d observational window or the higher harmon- The final Chandra observation was carried out just a month after the ics of the main peak and its 1-d aliases. The lower panel in Fig. 5 end of this season’s ground-based observations. However, based on shows the results of the BLS transform. The highest peak occurs the previous source activity evolution, it seems reasonable to assume at 4.4912 h with an uncertainty of ∼0.0004 h. The two periods are that the level of dust production was still quite substantial. roughly consistent to within the statistical uncertainties. The X-ray image produced from the sum of the four separate ex- It is worth noting that if any periodicities have an amplitude that posures is shown in Fig. 8; the image covers a 3 arcmin × 3arcmin is an order of magnitude lower than that of the prominent 4.4913 h region. The left-hand panel shows the raw X-ray image with all period reported here, it would not show up in either the L-S or BLS the individual detected X-rays displayed. The location of WD transforms as a significant signal. Thus, we can conclude that the 1145+017 is marked with a small green circle. The right-hand K2 ‘B-F’ periods, with the amplitudes found in the original K2 data panel shows the same image smoothed with a Gaussian kernel of (1/2 per cent), would not have been detected here. In this regard, 1.5 arcsec radius. While there are about half a dozen weak back- we note that the ‘B’ period did become much more prominent for ground X-ray sources in the image, there is actually only a single a couple of weeks in 2016 April–May (see G17). However, it was detected X-ray photon within 1 arcsec of the target location.

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Figure 7. The ‘activity’ level of WD 1145+017 from the time of its discovery with K2. ‘Activity’ is defined as the fraction of the flux, averaged over one 4.5-h period, that is extinguished by dust. The activity this season was the highest on record. The times of the Chandra observations are marked by the four arrows.

Figure 8. Chandra X-ray image of the 3 arcmin × 3 arcmin region centred on WD 1145+017. The exposure is 40 ks, and the energy band is 0.5–6 keV. The raw image is shown in the left-hand panel where all the individual detected photons are displayed. In the panel on the right, the X-ray flux has been smoothed with a kernel of 1.5 arcsec radius. The location of WD 1145+017 is indicated by the green circle of 3 arcsec radius. No significant X-ray detection is made of WD 1145+017, with a 95 per cent confidence upper limit of 3 × 10−15 erg cm−2 s−1.

5.2 Limits on X-ray flux and luminosity We then use the PIMMS software (Mukai 1993) to estimate the limits on the unabsorbed X-ray flux corresponding to Rx . We estimated The fact that only one X-ray is detected in 40 ks of exposure implies the unabsorbed flux in two energy ranges: 0.5–6 keV, which is fully that we are essentially dealing with an upper limit to the flux. If we covered by ACIS-S data and hence relatively insensitive to the hypothesize a mean count rate for the source of six photons in 40 assumed spectral shape of the object; and 0.1–100 keV, effectively ks, then the probability of detecting only 0 or 1 photon is only bolometric, which required extrapolation outside the ACIS-S energy 1.7 per cent. We therefore take six counts as a reasonable, high- range, and hence sensitive to the assumed spectrum. confidence, upper limit. This corresponds to a count rate, Rx of: We focus on single-temperature plasma emission computed with the APEC code (Smith et al. 2001) for different temperatures and an −1 20 −2 Rx  6/40300 = 0.00015 counts s . (2) assumed absorbing column of NH = 3 × 10 cm . At the highest

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Table 3. Chandra flux/luminosity limits on WD 1145+017.

a b b c d Model Parameter Absorbed flux limits Unabsorbed X-ray flux limits log Lx M˙ 0.5–6 keV 0.5–6 keV 0.1–100 keV 0.1–100 keV

APEC 1 keV 1.24 1.34 1.77 27.81 0.73 APEC 2 keV 1.23 1.30 1.74 27.80 0.71 APEC 5 keV 1.44 1.50 2.34 27.93 0.96 APEC 10 keV 1.53 1.59 3.16 28.06 1.30 APEC 20 keV 1.60 1.65 4.65 28.23 1.91 APEC 40 keV 1.63 1.67 7.02 28.41 2.88 APEC 64 keV 1.64 1.69 9.02 28.52 3.71 Bremss. 20 keV 1.56 1.61 4.80 28.25 1.97 Bremss. 40 keV 1.60 1.65 7.06 28.41 2.90

Bremss. 64 keV 1.62 1.66 8.90 28.51 3.66 Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 Bremss. 80 keV 1.62 1.67 9.74 28.55 4.00 BB 1 keV 1.71 1.73 2.02 27.87 0.83 BB 2 keV 2.10 2.11 5.38 28.29 2.21 PL α = 2 1.46 1.54 4.29 28.20 1.76 PL α = 1 1.71 1.74 31.7 29.06 13.0 Mediane – 1.60 1.65 4.80 28.2 2.0 aModels: APEC plasma; Bremss. = thermal bremsstrahlung; BB = blackbody; PL = power law. bThe units for the absorbed and unabsorbed flux are both 10−15 erg cm−2 s−1. The unabsorbed flux is given for two different energy ranges as indicated. c −1 Units of Lx are erg s ; assumes a source distance of 175 pc. dInferred upper limit on the accretion rate in units of 1011 grams s−1 under the assumption that the accretion luminosity comes out in the Chandra band (see Section 5.4), and that equation (6) holds. eMedian value of all the column entries. temperatures, plasma emission is dominated by the bremsstrahlung X-ray emission in the absence of accretion. However, X-ray emis- continuum, and the APEC model is only available up to kT = 64 keV; sion can be expected from WD 1145+017 because it is likely accret- we have therefore also included bremsstrahlung model spectra up ing the sublimated gaseous remains1 of the dust that we infer from to kT = 80 keV. These results are summarized in Table 3. the dips in optical flux. Accreting white dwarfs produce thermal, As discussed in the following sections, the APEC plasma model is optically thin, collisionally excited plasma emission above the sur- the one we prefer. However, since the spectral shape of the emission face and/or thermal, optically thick, blackbody-like emission from at these low accretion rates is quite uncertain, we also show in the heated (see Mukai 2017 for a review). Here, we rely Table 3 the conversion of our upper limit on the count rate to X-ray heavily on the well-studied accreting white-dwarf systems, mainly flux limit using several other typical model spectra. As suggested cataclysmic variables (CVs), extrapolating to lower accretion rates above and can be seen from the table, the derived limits on the from the systems with the lowest known accretion rates (see flux are not particularly sensitive to details as long as much of the Section 5.4). emission is contained within the Chandra band (∼0.5–6 keV) and is The X-ray properties of an accreting white dwarf differ markedly not severely absorbed. This point is discussed further in Section 5.4. depending on whether it has a magnetic field strong enough to Finally, for an adopted source distance of 175 ± 25 pc, we can control the accretion flow. There are high-resolution spectroscopic convert the X-ray flux limits to constraints on the X-ray luminosity. observations of WD 1145+017 (Xu et al. 2016) that did not exhibit The average of the log Lx values in Table 3 for different spectral any Zeeman splitting, yielding an upper limit on the magnetic field parameters leads to a limit on the 0.1–100 keV X-ray luminosity of of ∼10 kG (Dufour & Hardy, private communication). This is a factor of ∼1000 lower than typically found in magnetic CVs. To L  × 28 −1 x 2 10 erg s estimate the magnetic channelling of the ion flow, we utilize the which we discuss in more detail below. well-known dimensional-analysis result for the magnetospheric ra- In the following two Sections (5.3 and 5.4), we attempt to interpret dius of a rotating magnetized white dwarf with an orbiting collection of charged atoms: how the limit on Lx informs us about the mass accretion rate, M˙ , onto the white dwarf. This is by far the most difficult of the steps R ζ 2/7 GM −1/7M˙ −2/7B4/7R12/7, m ( wd) acc wd wd (3) needed to constrain M˙ . The relation between M˙ and Lx depends on such factors as the importance of the white-dwarf’s magnetic (see, e.g. Pringle & Rees 1972; Lamb, Pethick & Pines 1973; field, what fraction of the surface of the white dwarf experiences Kluzniak´ & Rappaport 2007)whereMwd, Rwd and Bwd are the accretion, the emission mechanisms and so forth. These are explored mass, radius and surface magnetic field of the white dwarf, M˙ is in Section 5.4 that enables us to estimate the limits on M˙ given in the accretion rate and ζ is a dimensionless factor that depends on the last column of Table 3. such quantities as the ratio of to orbital velocity and

5.3 Limits on mass accretion rates 1 We note, however, that in principle, larger objects, e.g. 100 µm, may The photosphere of WD 1145+017, with an resist sublimation and accrete directly on to the surface of the white dwarf, of 15900 K (V15) is far too cold to produce a detectable level of thereby depositing accretion energy directly into the surface layers.

MNRAS 474, 933–946 (2018) 942 S. Rappaport et al. solid angle subtended by the accretion flow. Plugging in illustrative studies, the parameter of choice is often the specific accretion rate parameter values for WD 1145+017, we find (accretion rate per unit area), m˙ acc, instead of M˙ acc.       The framework for interpretation in the case of magnetic CVs is ζ 2/7 M˙ −2/7 B 4/7 R R acc wd . the Aizu model (Aizu 1973), in which a free-falling (supersonic) m 18 wd − (4) 0.01 1011 gs 1 10 kG flow hits the white dwarf surface and forms a standing shock with By comparison, the corotation radius is a shock temperature, Ts, that is determined by the free-fall velocity     of the flow GM 1/3 P 2/3 R wd P 2/3 95 R , (5) GM m μ c π2 wd . 3 wd p 4 4 5h Ts = 8 Rs P      where is the period of the magnetic white dwarf normal- M 1.4R⊕ μ ized for convenience to the typical dip period, though this may well 68 wd keV, (7) 0.6M R 2 be, or not, the of the white dwarf. For motivation on s

why this choice for the rotation period might be of interest, see the Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 (see, e.g. Frank, King & Raine 1985)whereR is the radial distance recent model proposed by Farihi, von Hippel & Pringle (2017). s of the shock front (presumed to be near the white dwarf), m is the From the above estimates, we can see that the p proton mass and μ is the dimensionless mass per particle in the would lie within the corotation radius for a 4.5 h period2 unless the post-shock region. We take the post-shock material to be essentially magnetic field is  200 kG or if M˙  3 × 108 gs−1. Since neither acc fully ionized metals for which μ 2. While any contribution from of these seems likely, especially during the ‘high activity’ level of H would lower μ somewhat, it is probably nowhere as low as the this past observing season, we take the magnetospheric radius to typically assumed value of ∼0.6 that is appropriate for solar com- lie inside the corotation radius corresponding to 4.5 h. If the white position material. The post-shock plasma cools via bremsstrahlung dwarf is indeed rotating with a 4.5 h period, or longer, this would emission and the shock height is determined by the requirement that be considered a ‘slow-rotator’ in the language of accreting neutron the plasma cooling time equals the remaining infall time from the stars (see, e.g. Kluzniak´ & Rappaport 2007), which is capable of shock to the surface. accreting any charged atoms reaching the magnetosphere. Finally, In magnetic CVs, f is variously estimated to have values in the in this regard, we note for B  100 G, the ion magnetosphere wd 10−4–10−2 range, with m˙ of the order of 1 g s−1 cm−2,which would lie inside the white dwarf. acc places the shock close to the white dwarf surface. In this case, Because we have no firm estimate of either the white dwarf rota- roughly half the X-rays are absorbed by the white dwarf photo- tion period or its B field, we therefore proceed by assuming that WD sphere, and the remaining half provides the observed luminosity. 1145+017 can accrete either via a magnetically controlled accre- Unless f is much smaller in WD 1145+017 than in magnetic tion flow or via an accretion disc. Any accreting matter originating CVs, the specific accretion rate is likely very low (10−4 g from a 4.5 h orbit will retain either all, or half, of the kinetic energy cm−2 s−1). This should result in a large shock height and a post- it acquired from the gravitational potential, respectively, for the two shock plasma of much lower density than in magnetic CVs. In that cases. The maximum possible X-ray luminosity that is available case, only a negligible fraction of emitted X-rays would be inter- from the accretion luminosity is therefore: cepted by the white dwarf surface. On the other hand, we must GM M˙ consider the possibility that X-rays are not emitted at all. L wd acc . x (6) In principle, the post-shock plasma in WD 1145+017 could Rwd cool via cyclotron emission; however, it is likely to be in the × 28 −1 The upper limit on X-ray luminosity (2 10 erg s ;seeTable3) bremsstrahlung-dominated regime (Masters et al. 1977). If accre- M<˙ × 11 −1 then corresponds to 2 10 gs where we have taken the tion takes place predominantly in the form of dense blobs (Kuijpers + mass and radius of WD 1145 017 to be 0.6 M and 1.4 R⊕, & Pringle 1982), then it is possible to avoid the formation of a respectively. shock above the photosphere, instead liberating all the potential en- An important caveat, however, is that this limit holds only if the ergy below it. However, given the very low total accretion rate, this bulk of the released gravitational potential energy emerges in the scenario is unlikely unless strong density contrasts from individual X-ray band of the spectrum. At these low accretion rates on to a grains, which produced the gas, can survive. The large shock height white dwarf, this is a complicated issue. We next tackle the question itself will lower the shock temperature – in the extreme case, when of when, and under what conditions, the gravitational energy release the shock height approaches the magnetospheric radius, this will comes out predominantly in the X-ray band. result in an X-ray temperature that is a factor of ∼18 lower, i.e., ∼4 keV (see eqns. 4 and 7). It is possible that additional effects come into play that we have 5.4 In what energy band does the accretion luminosity not considered (e.g. how quickly can ions and electrons reach tem- appear? perature equilibrium, and what are the consequences of such a In the magnetic case, the flow inside the magnetospheric radius is two-temperature plasma?). confined by the magnetic field and accretion will occur on a rela- In the case of a Keplerian flow (i.e. in the non-magnetic case), tively small region (‘spot’) near the magnetic poles. The fractional the material will encounter a strong shock just above the white surface area of the spot, f, is as important in determining the out- dwarf surface. Its temperature is then determined by the Keplerian going radiation as is the total accretion rate, M˙ acc. In more recent velocity, or equivalently, the depth of the gravitational potential, and is Ts 35 keV for a 0.6 M white dwarf. At low accretion rates, the shocked gas is optically thin, and cools by emitting thermal 2 We reiterate that the rotation period of WD 1145+017 is unknown. How- X-rays (including atomic X-ray line emission) before settling on ever, in the Farihi et al. (2017) model, the rotation period of the white dwarf to the white dwarf. Therefore, the average temperature of X-ray must be 4.5 h. emitting gas is of order half the shock temperature.

MNRAS 474, 933–946 (2018) WD 1145+017 photometric & X-ray observations 943

Dwarf novae in quiescence are non-magnetic CVs with low ac- and its accretion. Finally, since we know that the dust production cretion rate, and their X-ray data generally agree with this sim- changes dramatically on a time-scale (see Fig. 7), we cannot ple expectation (Byckling et al. 2010), with typical luminosities even treat this set of steps as a steady-state process. of 1030–1032 erg s−1. However, at the lowest accretion rates, the Nonetheless, we will proceed to get a sense of what the ac- shock appears to be at a considerable height above the surface, and cretion rate might be. V15 estimated a dust production rate in hence at a lower temperature. GW Lib is the best-studied case with WD 1145+017 of 2 × 109–3 × 1010 gs−1. The dust-activity level a characteristic temperature of 2 keV and an X-ray luminosity of during the 2016–2017 season was, however, at least 40 times higher ∼1 × 1029 erg s−1 (Hilton et al. 2007). This suggests that the shock than in 2015 when it was first discovered. Thus, the dust mass-loss is located several white dwarf radii above the surface. Our count rate could well lie in the range of 1011–1012 gs−1 at the current rate-to-flux conversion for WD 1145+017 (see Table 3) allows for epoch. temperatures that are even this low. Here, we briefly review the arguments by which we infer the As discussed above, for either magnetic or disc accretion the dust mass-loss rate. During the interval over which the Chandra shock temperatures encountered in WD 1145+017 are plausi- observations were conducted, the mean flux depression over an bly confined to a range of 8–70 keV, and in the optically thin orbital cycle is close to 15 per cent. If the optimum dust grain cross- Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 case (which likely obtains), the mean X-ray emitting gas should section per unit mass occurs near 1 μm, then we can consider a have something of the order of half these temperatures. As we can sheet of dust that is 1 μm thick, covers the white dwarf’s diameter see from Table 3, the conversion factors from detected X-ray counts and is 15 per cent filled. If such a sheet runs around the entire orbit, to bolometric luminosity cover only a factor of ∼4 in range. There- the amount of mass it would contain is M 3 × 1016 g. fore, if we adopt a mean effective X-ray emitting temperature of A key unknown parameter is the lifetime of this dust. For kTemis 20 keV, we can set an upper limit on the X-ray luminosity dust grains larger than ∼2 μm, which may survive for weeks without L  . +1.7 × 28 −1 of x 1 7−0.8 10 erg s and a corresponding limit on the sublimating (see Xu et al. 2017), we can still estimate an upper limit M˙  +2 × 11 −1 mass accretion rate of 2−1 10 gs . The ranges on the to the grain lifetime in the following way. We tentatively assume limits reflect the uncertainty in the spectral models. that the dust emitted by the orbiting debris occupies a volume that is One potential complication that we have not addressed is the roughly the same size in the vertical (to the orbital ) direction absorption of X-rays by circumstellar matter, the latter of which is as in the radial direction. In that case, the dust clouds extend at least observed in the optical (Xu et al. 2016). In a medium with solar a white dwarf radius in the radial direction, or ∼1 per cent of the abundance, the most important elements for X-ray absorption are orbital radius. This would tend to lead to complete shearing of the C, N, O and Fe, and a concomitant column density of unbound material around the entire orbit within about 60 orbits, or the order of 1022 cm−2 is sufficient to alter the ACIS-S count rate- about 10 d.3 In fact, in order to maintain coherent dip structures as to-flux conversion factor by 2. Such a total column density will are seen in Figs 1 and 2, that are as narrow as 0.1 in orbital phase, have an Fe column density of 2 × 1017 cm−2. Xu et al. (2016) we can infer that the dust replenishment time must likely be as short 16 −2 report that the Fe II line has a column density of 10 cm ,soitis as a day. We postulate, therefore, that the dust that we see at any quite reasonable to expect that the total metal column density will be given moment must be replenished every day or so at a minimum  1017 cm−2, and will therefore not substantially alter our estimates mass-loss rate of ∼2 × 1011 gs−1. This is quite consistent with above. the ballpark range mentioned above, based on a simple ‘activity’ Finally, we show that even if a substantial accretion rate of scaling from the K2 discovery epoch. unsublimated matter rains down on to the white dwarf surface, This estimate of the lower limit on the rate of mass (from dust) the resultant thermal emission will always be very far below the that must ultimately be accreted by the white dwarf is just about Chandra X-ray band. The thermalized surface temperature due to the same as is the upper limit inferred from our X-ray observations. direct accretion over a solid angle  on to the surface of the white Therefore, the best we can say at the moment is that the X-ray upper dwarf is given by limit on M˙ is closely consistent with the lower limit on M˙ that is     inferred from dust sublimation rates that come from the observed GM M˙ 1/4 1/4 wd 1sr 1/4 dips in the optical flux. T , 3800 M˙ K, (8) wd ther σ R3  11 wd σ M˙ where is the Stefan–Boltzmann constant and 11 is the accretion 6 DISCUSSION rate in units of 1011 gs−1. Since this temperature is lower than that of the white dwarf itself, the resultant emission is nowhere near the In this work, we have assumed that the dips in photometric flux from + X-ray band. WD 1145 017 are caused by dust clouds circling around the white dwarf. It would seem that dust is the only efficient form of matter capable of blocking up to 60 per cent of the system light for intervals 5.5 Comparison to inferred M˙ based on dust of time longer than a major planet would take to transit the white dwarf. We presume that the origin of the dust is ultimately from Inferring the rate of mass accretion onto the white dwarf collisions or sublimation of small bodies, i.e. asteroids, orbiting the WD 1145+017 is at least a few steps removed from the observa- white dwarf. The passage of the dust clouds has characteristic pe- tions of periodic dips in the optical flux. The first step is to estimate riods of 4.5–4.9 h. In our judgement, these likely reflect the orbital the amount of dust present at any given moment, and from that the periods of the bodies that give rise to the dust. However, recently rate of mass-loss from the orbiting bodies in the form of dust. This an alternative idea has been put forth wherein the characteristic of course does not factor in any gas that is lost along with the dust. Once the dust is in orbit about the white dwarf, it has an uncertain lifetime against sublimation. From there, even assuming that the 3 This hinges on there being no significant B field for WD 1145+017; gaseous material ultimately makes its way down to the surface of see however Farihi et al. (2017) for an interesting scenario involving a the white dwarf, we do not know the time lag between its production substantially magnetised white dwarf.

MNRAS 474, 933–946 (2018) 944 S. Rappaport et al.

Table 4. Observed phenomena versus scenarios.

Phenomenon Dust emitting asteroidsa collisions b Magnetic shepherdingc

Long-lived dipsd Straightforward to explain Difficult to explain the persistence Tricky to explain but plausible Multiple periodse Straightforward to explain Straightforward to explain Difficult to explain Depth of dipsf Difficult to explain the depth Straightforward to explain Straightforward to explain Period stabilityg Partially straightforward Depends on numbers, masses of bodies Straightforward for one period Sudden eventsh Plausible Natural explanation Neutral Activity changesi Plausible Natural explanation Neutral Source of dust Natural explanation Natural explanation No explanation aEmission via sublimation, rotational instability, or thermal fracture; see also V15. bKenyon & Bromley (2017). cFarihi et al. (2017). dWeeks to months. Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 eThey range over 8 per cent in period. fUp to 60 per cent. gSee discussion below. hE.g., event ‘G6420’ in (G17). iSee Fig. 7. periodicity represents the rotation period of the white dwarf that  2000 yr (Feature 1 in Fig. 3). Feature 2 in Fig. 3 appears to have is presumed to be strongly magnetized. The concentration of dust a continuously changing period with P/P˙ 400 yr. For the larger at certain rotational longitudes would then be explained by mag- and more complex dips (Fig. 2 and Features 4–6 in Fig. 3), we can netic shepherding of charged dust grains of submicron size (Farihi envision a collection of small asteroids in a near common orbit, et al. 2017). each of which produces a dust . The dust clouds can overlap. We now proceed to list some of the empirical facts that we have As the small bodies evolve in size and position, their dust clouds learned about the photometric dips in WD 1145+017 from this drift slowly with respect to each other. work as well as from previous studies. A number of the dip features Due to the fact that any dust clouds capable of producing the and properties can be thought about in the context of (i) orbiting observed dips must necessarily be far outside any asteroid’s Hill asteroids; (ii) sublimation of, and collisions among, the asteroids sphere, there must necessarily be large shearing effects on the dust to produce dust clouds and (iii) possibly magnetic shepherding clouds. In the absence of any other shepherding , we expect of charged dust grains by an hypothesized strongly magnetized that the dust clouds would not last for more than a couple of days white dwarf. At present, there are no quantitative models that can before dissipating. If, in fact, the dust clouds quickly dissipate due to definitively relate any of these models to specific details of the shearing, we would expect that the dust must be continually replen- observations. Nonetheless, we will comment about the possible ished on this time-scale. However, in the scenario recently suggested applicability, or lack thereof, of some of the basic theoretical ideas by Farihi et al. (2017), if the dust grains are small (0.05 μm) and with the observational facts, as we see them. charged (due to UV bombardment), and the white dwarf has a sur- Some of the basic phenomena that we are trying to explain, along face magnetic field as large as ∼100 kG,4 the dust can be forced with different physical models, are summarized in Table 4.We to corotate with the star via the magnetic field. In that case, one discuss these in more detail below. would interpret the periodicity of the dust dips as being due to the Dip features are persistent from orbit to orbit (see e.g. Figs 2 underlying rotation period of the white dwarf rather than asteroid and 3). Some of the features evolve over days to weeks, but a few orbital periods. are present for at least 8 months (see Figs 3 and 4). The ‘A’ period, Empirically, the dust clouds are able to obscure up to ∼60 per cent and other periods within ±0.1 per cent of it, seem to be almost al- of the light of the white dwarf, but they have never been observed ways detectable from ground-based observations (V15;Gansicke¨ to block more than this apparent upper limit of 60 per cent. It re- et al. 2016; R16; G17). The ‘B’ period has been detected over only mains a mystery as to whether this indicates that the dust covers one two-week period from the ground (G17). The ‘C-F’ periods the entire star with a minimum transmission of 40 per cent, or if were seen only with Kepler K2, presumably due to their shallow the optical depth can become very high but never cover more than depths. Some large, i.e. deep and broad, dip features (perhaps ac- 60 per cent of the geometrical projected area of the white dwarf. In tually combinations of independent dip features) can last for up to order to block any substantial fraction of the white dwarf’s light, 30 per cent of an orbital cycle (e.g. Figs 1–3). Because these broad the dust cloud must extend away from the orbital plane by of the dips largely repeat from orbit to orbit, and can even persist for up order of 1/2◦ (as seen from the WD). Assuming that dust in at to several weeks (see Fig. 2), it is difficult to know whether they are least some deep dips arises from individual asteroids travelling at due to a single complex dust cloud or a collection of independent ∼300 km s−1, we conclude that the dust would have to be ejected dust clouds. It is also difficult to distinguish between dips simply with speeds of ∼3kms−1 or else the relatively large range of angular evolving in shape or being comprised of a set of dips with slightly different orbital periods. The most persistent dips produce lines on a waterfall plot that 4 The magnetic field in WD 1145+017 has not yet been measured well are consistent with being straight (e.g. Feature 1 in Fig. 3 and enough to know whether the magnetic model is viable, though recent indi- the unlabelled long vertical stripe in Fig. 4), i.e. representing a cations are that B  10 kG (Section 5.3). Moreover, recent measurements 5 period that is constant to within 2 parts in 10 .However,there of dust grain size by Xu et al. (2017) seem to indicate that very few, if any, are some indications of period changes on time-scales of P/P˙ of grains less than 1 µm are likely to remain in the dust clouds.

MNRAS 474, 933–946 (2018) WD 1145+017 photometric & X-ray observations 945 tilts could not be accommodated dynamically. Thermal velocities, This is comparable with the inferred rates of dust production in the i.e. involved in sublimation, would be inadequate to propel material system, and, by inference, the rate of that sublimated material on to far enough above the orbital plane. However, occasional collisions the surface of the white dwarf. However, we caution that the among orbiting asteroids could yield high-velocity fragments. An- of the accretion-induced X-ray spectrum at these low values of M˙ other explanation could involve the magnetic shepherding model of is not well understood (see Section 5.4), and a significant fraction Farihi et al. (2017) where small charged dust grains could fall in of the accretion energy may not come out in the X-ray band. towards the white dwarf while being channelled by the magnetic We do not yet have a good picture of the nature of the bodies field on to its poles. In the process, the grains could then naturally orbiting WD 1145+017. However, it is clear that the dust clouds reach high latitudes on the white dwarf. change on time-scales of weeks to , and persistent monitoring Eventually, the dust grains must sublimate or be dragged in to- may yet reveal the number of bodies producing the dust clouds and wards the white dwarf via Poynting–Robertson effect. In the Farihi a better estimate of their masses. et al. (2017) scenario, the small charged dust grains would naturally Data files for all of the ground-based photometric observations fall towards the white dwarf surface as they cross the magneto- presented in this work are available upon request from author BLG. sphere and are swept up by the magnetic field.5 Presumably, the These files include normalized fluxes for the light curves, as well Downloaded from https://academic.oup.com/mnras/article/474/1/933/4563657 by guest on 03 October 2021 dust grains would sublimate before they ever hit the white dwarf as their dip solutions (BJD, depth, ingress time, egress time). Web surface. Obviously, the details of all these processes, as they oper- page URLs are also available from BLG that show all light curves ate in WD 1145+017, are highly uncertain. However, some of the in detail and in several formats. gas that results from sublimation becomes ionized and finds itself moving at high speed around and towards the white dwarf. We can speculate that it is this high-velocity gas that may be responsible for ACKNOWLEDGEMENTS the broad absorption line features seen in high-resolution spectral We thank Paul Benni and Tom Kaye for providing a few of the observations (Xu et al. 2016; Redfield et al. 2017). light curves and for helpful discussions. SR and BLG acknowledge As we have shown in Section 5.3, if WD 1145+017 has a sur- partial support from National Aeronautics and Space Administra- face B field above ∼100 G, the magnetosphere for gas ions would tion (NASA) Chandra grant GO7-18008X. AV was supported by lie outside the white dwarf (see equation 4). Once the ions cross the National Foundation (NSF) Graduate Research Fellow- the magnetosphere, they will be forced to corotate with the white ship, grant no. DGE 1144152, and also acknowledges partial sup- dwarf, whatever its rotation period may be (perhaps even 4.5 h; Far- port from NASA’s Transiting Exoplanet Survey (TESS) ihietal.2017). The inferred rate of gas release from sublimating mission under a sub-award from the Massachusetts Institute of − dust grains could be as high as 1012 gs 1 (see Section 5.5) during Technology to the Smithsonian Astrophysical Observatory, Spon- the most active intervals of WD 1145+017. The upper limit on the sor Contract Number 5710003554. This work was performed in  × 28 −1 X-ray luminosity of Lx 2 10 erg s is marginally consistent part under contract with the California Institute of Technology with the estimated lower limit on M˙ inferred from the dust transits. (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA As a guide to future X-ray observations, we note that the accretion through the Sagan Fellowship Program executed by the NASA of the gas ions is highly likely to take place via magnetic funnelling. Exoplanet Science Institute.

7 SUMMARY AND CONCLUSIONS REFERENCES

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